in the space. The notion of "space" is intuitive, since each x_i (i = 1, 2, ..., n) can have any value, the collection of values defines a point in space.

The dimension of the position space is n (also denoted dim(R) = n). The coordinates of the vector r with respect to the basis vectors e_i are x_i. The vector of coordinates forms the coordinate vector or n-tuple